When you fight a monster, You'll see a combo gauge, it's 7 white circle. Whenever you use a skill to the monster, one icon will appear at the gauge. The icon will be the same color as the skill's color. If you use another skill to the monter, and your second skill has different color than the first one, another icon will shown up at the gauge. About 1~2 second after the 2nd skill, a small explosion will hit the monster, that is your bonus damage for the combo.

The holic's site says that after you fill up all 7 combo gauge with 7 different color skill, a short animation will appear, but it seems haven't implemented yet .

But of course you can have fun with filling it up ^^. You need to be in a party to do so, because there's no job have 7 different color skill (each job usually have 4~5 color). But if you like to try it yourself, maybe you can try to change your job in the middle of the battle.